Long-term sickness absence episodes which did not end at 31 www.selleckchem.com/products/ly333531.html December 2001, or which could not be recorded because the employee left employment, were right censored. Statistics Survival data were plotted using SPSS life tables. The rates of onset of long-term sickness absence and return to work were
parameterized using Transition Data Analysis (TDA, version 6.4f). The time to onset of long-term absence was recorded from days into weeks. The duration of long-term sickness absence was counted in days, but to make the calculations possible, 42 days were selleck chemicals llc subtracted from the absence duration, in order to obtain 1 as the lowest value. We investigated the following models (Blossfeld and Rohwer 2002): (1) Exponential model: the hazard rate can vary with different sets of covariates, but is assumed to be time constant; the hazard function and survivor function are r(t) = a, respectively G(t) = exp(−at), with t = time and a = constant. (2) Gompertz–Makeham model: the hazard rate increases or decreases monotonically with time. The hazard function is given by the expression r(t) = a + b exp(ct), in which a, b and c are constants and t = time. For long durations the hazard rate declines towards the value of parameter a (the
Makeham term). If b = 0 the model reduces to an exponential Selleckchem Ro 61-8048 model r(t) = a, which states the hazard rate is constant over time. The parameter c is the shape parameter. If the parameter c is negative, we conclude that Exoribonuclease increasing duration of the process leads to a declining hazard rate. If the parameter c is positive, increasing duration leads to an acceleration of the hazard rate. (3) Weibull model: the hazard rate increases or decreases exponentially with time: r(t) = ba b t b − 1, but like the Gompertz model, it can also be used to model monotonically decreasing (0 < b < 1) or increasing rates (b > 1). An exponential model is obtained in the special case of b = 1. (4) Log-logistic model: this model is even more flexible than the Gompertz and Weibull distributions. The hazard rate function is: $$ r(t
)= \fracba^b t^b – 1 1 + (at )^b $$For b ≤ 1 the hazard rate monotonically declines (Gompertz–Makeham) and for b > 1 the hazard rate rises monotonically to a maximum and then decreases monotonically. Thus this model can be used to test a monotonically declining time-dependence against a non-monotonic pattern. This is the most commonly recommended model if the hazard rate is bell-shaped. (5) Log-normal model: this model implies a non-monotonic relationship between the hazard rate and the duration; the hazard rate increases to a maximum and then decreases. (6) Generalized gamma models can be used to discriminate between exponential, Weibull and log-normal models. It has three parameters: a, b and k of which a can take all values, but b and k must be positive.